So much for the false claim by the Kotel's haredi Rabbi Shmuel Rabinowitz about what the authentic custom at the Kotel really is.
The Israel section of this video starts at about 4 minutes in. The prayers at the Kotel start about 9 minutes in.
The haredim appear to be reciting Psalms and personal prayers. Perhaps for formal prayer services, the men and women were separated by more space. (The Ottomans and the British did not allow a mechitza in those days, I think.)
Nevertheless, the men and women did pray together informally, as this video proves: